By way of example, document FR-2 504 788 discloses a makeup device in which a reservoir is provided in its neck with a wiper having at its bottom end radial tongues that, at rest, lie in a plane extending perpendicularly to a direction in which the applicator is extracted from the reservoir. The free ends of the tongues are spaced apart from one another so as to leave a circular opening in the center of the wiper. Such an arrangement makes it possible, while extracting the applicator from the reservoir, to remove any excess makeup from the surface of the brush. Nevertheless, makeup accumulates at the free end of the brush, from which makeup is poorly eliminated by the wiper because of the central orifice in the wiper. This drip of excess makeup, or “glob”, must nevertheless be eliminated by the user prior to putting the applicator into contact with the eyelashes, since otherwise the drip would become deposited as a whole on the eyelashes. It turns out to be awkward for the user to eliminate this drip from the brush insofar as the user usually holds the reservoir in one hand and the applicator in the other. The user may attempt to remove the glob by putting the end of the applicator into contact with the inside of the neck, but not only is this operation awkward to perform, it is not certain to achieve the desired result.